# Magnetic Field Strength H

The magnetic fields generated by currents and calculated from Ampere's Law or the Biot-Savart Law are characterized by the magnetic field B measured in Tesla. But when the generated fields pass through magnetic materials which themselves contribute internal magnetic fields, ambiguities can arise about what part of the field comes from the external currents and what comes from the material itself. It has been common practice to define another magnetic field quantity, usually called the "magnetic field strength" designated by H. It can be defined by the relationship

H = B00 = B/μ0 - M

and has the value of unambiguously designating the driving magnetic influence from external currents in a material, independent of the material's magnetic response. The relationship for B can be written in the equivalent form

B = μ0(H + M)

H and M will have the same units, amperes/meter. To further distinguish B from H, B is sometimes called the magnetic flux density or the magnetic induction. The quantity M in these relationships is called the magnetization of the material.

Another commonly used form for the relationship between B and H is

B = μmH

where

μ = μm = Kmμ0

μ0 being the magnetic permeability of space and Km the relative permeability of the material. If the material does not respond to the external magnetic field by producing any magnetization, then Km = 1. Another commonly used magnetic quantity is the magnetic susceptibility which specifies how much the relative permeability differs from one.

Magnetic susceptibility χm = Km - 1

For paramagnetic and diamagnetic materials the relative permeability is very close to 1 and the magnetic susceptibility very close to zero. For ferromagnetic materials, these quantities may be very large.

The unit for the magnetic field strength H can be derived from its relationship to the magnetic field B, B=μH. Since the unit of magnetic permeability μ is N/A2, then the unit for the magnetic field strength is:

T/(N/A2) = (N/Am)/(N/A2) = A/m

An older unit for magnetic field strength is the oersted: 1 A/m = 0.01257 oersted

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